Finite element and in vitro study on biomechanical behavior of endodontically treated premolars restored with direct or indirect composite restorations

Objectives of the study were to investigate biomechanical properties of severely compromised premolars restored with composite restorations using finite element analysis (FEA), and in vitro fracture resistance test. A 3-D model of an endodontically treated premolar was created in Solidworks. Different composite restorations were modelled (direct restoration-DR; endo-crown-EC; post, core, and crown-C) with two different supporting tissues: periodontal ligament/alveolar bone (B), and polymethyl methacrylate (PMMA). Models were two-point axially loaded occlusally (850 N). Von Mises stresses and strains were calculated. The same groups were further tested for static fracture resistance in vitro (n = 5, 6.0 mm-diameter ball indenter, vertical load). Fracture resistance data were statistically analyzed (p < 0.050). The highest stresses and strains in all FEA models were observed on occlusal and vestibular cervical surfaces, corresponding to fracture propagation demonstrated in vitro. C showed the lowest stress in dentin, while EC showed lower stresses and strains in crown cement. B models demonstrated larger high stress areas in the root than PMMA models. No significant differences in fracture resistance (N) were observed between groups (DR: 747.7 ± 164.0, EC: 867.3 ± 108.1, C: 866.9 ± 126.3; p = 0.307). More conservative restorations seem a feasible alternative for endodontically treated premolars to conventional post-core-crown.


FEA. Maximum von Mises stress values. The maximum von Mises stresses in the investigated models are
presented in Table 1. The maximum stresses in the restorations were found to be similar in all the groups, while in the dental tissues, certain differences were evident among the groups. The stresses in dentin were lower in the indirect restorations compared to the direct restoration (DR > EC > C) regardless of the supporting tissue used. The stresses in the enamel were higher in the EC compared to DR, and slightly higher in all the models with the PMMA support. In the root portion of the C model, higher stresses were found in dentin and the restorative materials in the B supported model, compared to the one embedded in PMMA.
Von Mises stresses distribution. The highest stress areas were distributed similarly in the crowns of all the tested models: on both cusps, on the occlusal central fissure, as well as on the cervical segment of the enamel and dentin, particularly the vestibular portion. In the DR and EC models, the stress distribution was similar, however, there were certain differences between these two restoration types and the C models. Although the occlusal stress distribution in all the models was similar, the crown-restored models showed a slightly smaller area under high stresses in the cervical vestibular segment (Figs. 1, 2).
Interestingly, although the maximum stress values were similar, the distribution of stresses was different between the groups having B as supporting tissue, compared to the PMMA. There were larger areas of high stresses in the root portion of all the models supported by B (Fig. 3). The most prominent differences can be noted in the CB model, where the highest stresses in dentin were not distributed at the cervical vestibular portion of the root as in the CPMMA and all the other investigated models, but were located on the bottom of the post cavity preparation.  Table 2. The strains were the highest in the crown restorations of all models, regardless of the supporting tissue simulation option. All the investigated models had similar crown restoration strain values. Similarly to the stresses, the strains in dentin were to the most part comparable in the DR and EC models, while they were lower in the C models. Interestingly, the strains in enamel in the EC groups were 3 times lower compared to the DR groups. EC also showed ~ 35% lower strains in the crown cement compared to C groups. Further, there were differences in the strain values between the CB and CPMMA groups in the root portion of the model, with the CB group demonstrating higher strains. The maximum strain values were distributed in the same manner as the maximum stresses. Hence, the highest strain in the CB model in dentin was located on the bottom of the post preparation, while in the CPMMA model it was on the cervical vestibular portion of the root, similarly to all the other models.
Static fracture resistance test: in vitro validation. The results of the one-way ANOVA test presented in Table 3 showed no statistically significant differences in the static fracture test values between the three tested groups (p = 0.307).
The evaluation of the fracture modes was performed by three different evaluators using a stereomicroscope. The agreement between the evaluators was 100%, and the results showed that in all the teeth restored with an EC fractures were unrestorable, followed by 20% and 40% of restorable fractures in the C and the DR groups, respectively (Table 3, Fig. 4).
The failure of the teeth in the in vitro study occurred in the portion of the teeth that corresponded to the high stress areas of the FEA model-started on the occlusal surface on the inner slope of the buccal cusp near the central fissure and propagated towards the vestibular cervical portion of the tooth.

Discussion
The results of the present FEA study demonstrated differences in the maximum von Mises stress and equivalent strain values in dental tissues and restorations within the investigated groups depending on the restoration type and the supporting tissue modeling. Hence, the first and third null hypotheses were rejected. Further, the type of restoration as well as the modeling of the conditions surrounding the tooth induced differences in the www.nature.com/scientificreports/ distribution of the maximum stresses in dentin, with possible implications in the clinical setting. Therefore, the second and fourth null hypotheses were also rejected. Maximum von Mises stresses and their distributions were similar in the coronal restorations of all the FEA models investigated in the present study, while strains were slightly lower in the indirect restorations. This corresponds to the results of the fracture resistance test, since there were no statistically significant differences between the tested groups although the mean fracture resistance was lower in the DR group. These results are in accordance with several FEA and in vitro studies 14,26,27 , while certain authors reported higher fracture resistance and lower stresses in premolars restored with endocrowns compared to the conventional crowns 28,29 . Contrary to this, another study 30 showed lower survival rate of premolars restored with endocrowns.
While the previously mentioned reports available in the literature 14,[26][27][28][29][30] are contradictory, a more detailed analysis of the interplay between stress and strain values and distributions in the models of the present study could offer interesting inputs. Firstly, crown-restored models showed lower von Mises stresses and equivalent strains in dentin compared to the DR and EC. Although this could lead to the conclusion that the post, core and crown restoration could clinically show better preservation of the dental tissues, note should be taken of the location of the maximum stresses. In the CB group, maximum von Mises stresses in dentin could be noted on the bottom of the post preparation cavity, rather than on the vestibular cervical portion of the tooth as in the other investigated groups. It seems that the post absorbed a certain amount of the stresses, but also transported them to the root portion of the tooth, and could hence potentially act as a wedge leading to catastrophic tooth fracture, as demonstrated in vitro 31 . This is in accordance with the report of a reduced stress concentration on the inner wall of the root in premolars restored with an endocrown compared to a post, core and crown restoration 32 . In general, post, core and crown restorations tend to undergo catastrophic root fractures more often compared to endocrowns 22 . Actually, it was demonstrated clinically that post placement can reduce the failure of post-endodontic restorations only within severely compromised teeth (when no coronal walls are present), and might therefore not be necessary in teeth with some of the tooth tissues preserved 9 . These affirmations are valid for traditional FRC posts, but customized posts have emerged in recent years, and could potentially offer better retention of the coronal restoration, while preserving the anatomy of the root canal and tooth tissue. It was demonstrated in vitro that there could be benefits to the use of auxiliary posts and/or composite resin relined posts in terms of fracture strength and failure pattern, as well as bond strength to root dentin, possibly due to a reduction in the thickness and defects of the cement layer [33][34][35] . FEA generated stress distribution in incisors www.nature.com/scientificreports/ showed a more favorable pattern compared to traditional systems 36 , but FEA studies in premolars on this issue are currently lacking. Further, in comparison to the crown cement in the C models, the cement of the EC models demonstrated around 35% lower von Mises stresses and strains, probably due to the geometrical differences between these two types of crowns. Endocrown is a more massive monolithic restoration, protecting the underlying cement layer from the direct influence of the occlusal loads, as also shown previously 37 . This could indicate that the full   www.nature.com/scientificreports/ crowns may be more prone to debonding compared to endocrowns. Moreover, stresses in the enamel of the DR models were slightly lower than that of the EC models. However, the strains were 3 times lower in the enamel of the EC models. Actually, the crown cement layer in the EC models showed a similar maximum strain value as the enamel in the DR models. Hence, it seems that the cement layer "buffered" the strain of enamel under the endocrown, possibly due to the lower elastic modulus compared to both the crown and the enamel, which could lead to better preservation of the enamel tissue during fatigue loading in teeth restored with endocrowns compared to direct restorations 3 .
The majority of samples in all groups failed in a similar manner in the static fracture test, with the crack initiation at the inner slope of the buccal cusp, near the central occlusal fissure, and the fracture most often reaching the cervical vestibular region of dentin under the cement-enamel junction (CEJ). This failure mode corresponds to previously published studies [38][39][40][41] . The distribution of high stresses found in the present FEA study in the models embedded in PMMA (under a load that corresponded to the mean fracture load in the static fracture resistance test), revealed a distribution which is in accordance with the fracture propagation of the in vitro study. The areas under the highest stresses were the loading positions on the inner slopes of the cusps, the central fissure, and the cervical vestibular portion of the tooth tissues. There were larger areas of high stresses in the models restored with the DR and the EC compared to the C restored model. Interestingly, the distribution of high stress areas in dentin changed when the PDL and the supporting bone tissue were modelled. There were larger areas under medium level stresses in the root portion of the teeth, and in the C model, the highest stress area moved from the vestibular cervical portion to the bottom of the post preparation cavity. This could further imply (along with the maximum von Mises stress and strain values) that clinically, the post could cause a wedge and lead to root fracture 22,31 . A recent review on validated FEA studies in dentistry reported that although the teeth in the in vitro validation experiments were mostly embedded in epoxy resin, composite resin, or silicone, in the corresponding FEA study, PDL and/or bone were modelled 25 . Hence, up to the authors' knowledge, this is the first study to investigate both supporting tissue options, that would correspond to the in vivo, as well as in vitro experimental setting.
Clinically, full crown restorations have similar failure rates in premolars and molars 22,30,42 . With the development of the minimally invasive dentistry concept, the preservation of tooth tissue has become a matter of utmost priority 2,43 . Hence, direct restorations and restorations such as endocrowns, modelled to preserve healthy tooth tissues and yet keep the retentive form, have been developed and promoted in the recent years. However, clinically, endocrowns seem to fail at a higher rate in premolars compared to molars 30 , even though these differences are not always statistically significant 16 . Restoration of endodontically treated premolars is challenging due to their morphology and specific position in the tooth arch. Premolars are exposed to more elevated loads than anterior teeth, both in the axial and shear directions, but have a smaller crown and steeper cusps compared to molars and are therefore more fragile, especially after a large portion of the tissue is lost 28,44,45 . Further, the pulp chamber of premolars, providing retention to the endocrown, is considerably smaller compared to molars.
A recent systematic review on the clinical performance of endocrowns in premolars demonstrated that this type of restoration preforms equally well as full crowns in FEA and in vitro studies, but not in a clinical setting 22 . This could be due to several factors. Firstly, the static fracture that is commonly used in the in vitro studies is unlikely to occur in the patient's mouth. The failure of restorations during intraoral use is nearly always due to fatigue 46,47 . Accordingly, it was demonstrated that bond strengths of posts to root dentin were significantly influenced by thermal 48 or thermomechanical aging 49,50 , which was not considered in the present research. Further, as demonstrated in the present study, the distribution of the stresses within the tooth-restoration complex is influenced by the supporting tissue modeling, and in vitro studies cannot fully replicate the intraoral setting, nor can they replicate the actual tooth loading conditions during mastication. The static FEA studies on the other hand, allow for a more accurate replication of the intraoral conditions regarding the supporting tissue and tooth loading conditions. However, apart from not accounting for model fatigue, they also usually omit another clinically important factor-operator sensitivity of the adhesive techniques, since perfect bonding is assumed, the Holy Grail not easy to achieve clinically 51,52 . Bonding to root dentin is even less predictable compared to the coronal dentin 53 . It was shown that the currently available luting agents cannot hermetically seal the endodontic cavity 54 . Nevertheless, by simulating perfect bonding, FEA allows researchers to focus on a specific factor that needs to be investigated without interference of other factors. Conversely, the results of in vitro studies can be In the present study, we opted to evaluate the Von Mises criterion, a scalar stress measure combining three principal stress values, identifying the areas of the model that are under highest stress and are consequently more prone to failure. This criterion enabled us to evaluate whether the critical areas identified in FEA matched the localization of fracture initiation and propagation of the in vitro specimens, as well as to compare our results with other published studies that used the same criterion 37,39 . Indeed, the calculation of principal stresses could provide a more detailed analysis of the tensile, compressive and shear stress components, and this could be considered a limitation of our study. Further, the sample size of the in vitro section of the present study (n = 5) could be considered low for mechanical testing. However, we performed a sample size calculation and used the recommended sample size. The in vitro part of the study was not performed as a standalone test, but as a complementary experiment to validate whether the propagation of fracture coincides with the stress and strain values and distribution that was demonstrated in the FEA, the main focus of the present study. Moreover, numerous published FEA studies used as much as 4 or 5 teeth for in vitro validation [55][56][57][58] .
We can conclude that, in terms of response to static axial loads, direct composite restoration, composite endocrown, as well as post, core and crown seem to be adequate for the restoration of endodontically treated premolars with a severe tissue loss. When a 2 mm ferrule is present, endocrowns demonstrated certain advantages in terms of stresses and/or strains values and distribution in tooth tissues and in the cement layer compared to the other restoration types. Furthermore, differences in the simulation of the supporting tissues can influence the results of FEA studies and should be taken into consideration, particularly when employing a FEA and in vitro experiment in the same study. Materials were considered to be linear, elastic and isotropic, and material properties were assigned to all the tooth tissues and materials (Table 4). www.nature.com/scientificreports/ In the present study, an axial load of 850 N was applied to 2 points, on the inner slopes of both cusps, to simulate the loading performed in the in vitro fracture resistance testing. The model was fixed in all directions on the outer surface of the bone/bone-simulating PMMA. Perfect bonding between the parts of the models was assumed. Curvature based high-quality meshing was performed and 136,513-229,599 nodes and 87,467-146,189 elements were obtained. Parabolic tetrahedral solid elements were used for meshing, as they enable higher quality meshing for irregular-shaped objects, such as biological tissues. The maximum element size was 2.30906 mm, minimum element size was 0.230906 mm. There were 0.0606-0.268% of the elements with the aspect ratio greater than 10, with 95-96.5% of the elements having a ratio lower than 3. Consecutively, numerical analysis was performed in the "Simulation" add-in of Solidworks. Von Mises stresses and equivalent strains were calculated and recorded.

Methods
Static fracture resistance test: in vitro validation. The dental materials used in the present study were donated by Coltène/Whaledent (Altstätten, Switzerland), unless stated differently. All the materials have been used by two experienced clinicians (T.M., A.C.), strictly following the manufacturer's instructions.
Fifteen extracted single-rooted premolars (sample size calculated using G*Power 3.1.9.7 for Windows: effect size f = 1.9191754, α error probability = 0.050, power (1-β error probability) = 0.800) were selected and treated endodontically with rotary instruments up to the file size 25 (Mtwo; Sweden & Martina, Due Carrare, Italy) and obturated with gutta-percha (Mtwo gutta; Sweden & Martina, and Gutta percha bar; Meta Biomed, Mülheim an der Ruhr, Germany). Teeth were further prepared in a standardized way, removing the crown leaving 2 mm of sound dentinal tissue in the cervical area above the CEJ. Premolars were randomly divided into three groups (n = 5) according to the protocol employed for the crown restoration, following the FEA groups: DR: (control)-Selective enamel etching was performed for 30 s with a 37% phosphoric acid (Etching), followed by adhesive resin (One Coat 7 Universal) application and light-curing for 20 s with a LED curing light (Valo; Ultradent, St Louis, MO, USA). The same curing unit was used in all restorative procedures for all the specimens. Further, a direct resin composite restoration (Synergy D6) was stratified in 2 mm-thick layers and each layer was polymerized for 40 s. The occlusal anatomy was created using a transparent silicone mold (Elite Glass; Zhermack, Badia Polesine, Italy) that was made prior to the treatment of the tooth. The composite was polymerized through the silicone mold for 40 s from each side, then the mold was removed, and the curing procedure was repeated.
EC: Three mm of the gutta-percha endodontic filling was removed from the cervical portion of the tooth to prepare the canal space for the retention of a CAD/CAM composite endo-crown (Block Brilliant Crios; crown wall thickness < 5 mm) fabricated using a milling system (CEREC; Dentsply-Sirona, Charlotte, NC, USA). The luting surface of the crown was sandblasted for 20 s at 1,5 bar pressure with 50 μm particles of sodium bicarbonate (Rondoflex; KaVo Dental, Biberach an der Riss, Germany) washed with water for 20 s, dried with an air flow for 2 s and immerged in an ultrasound bath (Transsonic T460/H; Elma Schmidbaue, Singen, Germany) for 5 min in a 50% ethanol solution (Ethanol; Carlo Erba Reagents, Cornaredo, Italy). Further, an adhesive resin (One Coat 7 Universal) was placed on the composite crown and on the tooth structure. The adhesive was light cured for 20 s only on the tooth surface, and the crown was cemented using a dual cure resin cement (DuoCem). Final light curing step was performed through the crown from each surface of the restoration.
C: The remaining coronal portion of the tooth was prepared for a composite crown (cervical margin of 1 mm, occlusal thickness 1.5-2 mm, 1-1.5 mm axial wall thickness). Teeth were restored with a glass fiber-based composite post (ParaPost Taper Lux), cemented with a dual cured resin-based luting material (DuoCem) 8 mm into the depth of the canal, and polymerized for 30 s using a LED curing unit. Further, a self-etch adhesive system was applied to the tooth structure (Parabond with Non-Rinse Conditioner), followed by a composite build-up (ParaCore Dentin) polymerized for 60 s using a LED curing light. The tooth preparation was finished, and a CAD/CAM composite crown (Block Brilliant Crios) was milled, sandblasted, luted with a universal adhesive (One Coat 7 Universal) and a dual cure resin-based luting cement (DuoCem), and polymerized for 20 s on each side, the same as in the EC group. www.nature.com/scientificreports/ Further, lateral static fracture resistance test was performed after 30-days storage in artificial saliva (KCl 0.9639 g/L, KSCN 0.1892 g/L, Na 2 SO 4 ·10H 2 O 0.763 g/L, NH 4 Cl 0.178 g/L, CaCl 2 ·2H 2 O 0.2278 g/L, NaHCO 3 0.6308 g/L, ZnCl 2 2.726 mg/L, HEPES 1.186 g/L, pH 7.4) at 37 °C. The roots of the teeth (2 mm under the CEJ) were embedded in methacrylate resin (Impression Tray Resin LC; Henry Schein, Services, Langen, Germany) and the teeth were mounted in a universal test machine (Instron 10-S; Instron, Norwood, MA, USA) at a 45° inclination to the long axis of the tooth. A metal rod with a spherical tip of 6.0 mm diameter was used to apply a vertical static load at a crosshead speed of 0.5 mm/min until the fracture of the specimens occurred.
Further, fractographical analysis of the failure areas was performed under a stereomicroscope (Stemi 2000-C; Carl Zeiss Jena, Germany) at a 30× magnification. The fractures that involve the CEJ or the tooth structure bellow the CEJ were considered unrestorable, while the fractures above the CEJ were considered restorable.
Since the normality (Shapiro-Wilk test), and homoscedasticity assumptions (modified Levene test) were not violated, the data were statistically analyzed using a one-way ANOVA and post-hoc Bonferroni tests with the significance level set at α = 0.050 (Stata; StataCorp, College Station, TX, USA).

Data availability
The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.